Cohomology of Drinfeld Modular Varieties, Part 1, Geometry, Counting of Points and Local Harmonic Analysis

by Gérard Laumon

Overview

Cohomology of Drinfeld Modular Varieties aims to provide an introduction to both the subject of the title and the Langlands correspondence for function fields. These varieties are the analogs for function fields of Shimura varieties over number fields. This present volume is devoted to the geometry of these varieties and to the local harmonic analysis needed to compute their cohomology. To keep the presentation as accessible as possible, the author considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. It will be welcomed by workers in number theory and representation theory.

Product Details

ISBN-13:	9780521172745
Publisher:	Cambridge University Press
Publication date:	12/09/2010
Series:	Cambridge Studies in Advanced Mathematics , #41
Edition description:	Reissue
Pages:	360
Product dimensions:	5.90(w) x 8.90(h) x 1.00(d)

Table of Contents

1. Construction of Drinfeld modular varieties; 2. Drinfeld A-modules; 3. The Lefschetz numbers of Hecke operators; 4. The fundamental lemma; 5. Very cuspidal Euler–Poincaré functions; 6. The Lefschetz numbers as sums of global elliptic orbital integrals; 7. Unramified principal series representations; 8. Euler-Poincaré functions as pseudocoefficients of the Steinberg relation; Appendices.

Editorial Reviews

A graduate text book, introducing not only the title subject, but also the Langlands correspondence for function fields, which are the analogues for function field of Shimura varieties over number fields. The first volume is devoted to the geometry of the varieties and to the local harmonic analysis needed to compute their cohomology. Little is revealed about the second volume except that the notion of very cuspidal function plays a crucial role in it. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"...these two volumes contain many results that are new and important....they are also the best source available for learning about the approacj to zeta functions via the theory of automorphic representations. They contain a wealth of information, theorems, and calculations, laid before the reader in Laumon's superb expository style....these two volumes are a welcome addition to the literature on automorphic representations and are highly recommended." Jonathan David Rogawski, Mathematical Reviews

From the Publisher